Turkish jets will continue to take part in the air operation backing Iraqi forces and Kurdish Peshmerga to retake Iraq's second city of Mosul from jihadists after the defence minister said late Tuesday Ankara had agreed a deal with its coalition partners.

"We have agreed with coalition forces for our air forces to take part in the Mosul operation," Fikri Isik was quoted as saying by the official Anadolu agency.

"Without Turkey, it is impossible to make decisions on the future of Mosul," he added during a visit to Rome.

His comments were further clarification of Turkey's future involvement after Prime Minister Binali Yildirim said earlier in the day that the country's jets joined in the air operation to recapture the city from the Islamic State group.

"Our air forces took part in the coalition forces' air operations in Mosul," Yildirim told his ruling Justice and Development Party (AKP) parliamentary group in Ankara.

Yildirim, who admitted he did not know "the operational details", told reporters afterwards there was agreement "in principle" to be part of the coalition.

The long-awaited offensive began Monday with air and ground support from a US-led coalition. Yildirim said Turkey was "closely-watching" what was happening but did not give details on the nature of the Turkish air support.

Mosul was captured by IS jihadists in June 2014. But ahead of the offensive, Turkey and Iraq were entangled in a war of words over Turkey's presence in northern Iraq.

Yildirim repeated President Recep Tayyip Erdogan's comments from Monday that Turkey would be involved in the operation and will be "at the table".

While insisting it cannot be left out of the operation, Turkey has often spoken of its fears over the potential involvement of Shiite militias and anti-Ankara Kurdish militia in the fight for mainly Sunni Mosul.

- 'Don't act tough with us' -

In a separate speech in Ankara, Erdogan said Turkey did not want to be party to any sectarian conflict in Iraq, but spoke of his concern for "our Sunni Arab brothers, our Turkmen brothers".

Earlier this month, Erdogan and Iraqi Prime Minister Haider al-Abadi traded barbs over Turkey's presence in Bashiqa in northern Iraq, where, according to Erdogan, nearly 700 Turkish soldiers are based.

Erdogan insisted Turkey had a historical responsibility to be in Iraq, referring to Mosul's past as part of the Ottoman Empire.

"We will be (present) on the ground and we will be at the table," Erdogan said.

Erdogan told the Iraqi government that "rather than acting tough with us" it should "deal" with other extremist groups like IS.

Foreign Minister Mevlut Cavusoglu said an Iraqi delegation was due to arrive in Turkey towards the end of the week -- "maybe Thursday -- as diplomats try to de-escalate the tensions.

"Both sides essentially have the will to solve this through dialogue," Cavusoglu said Tuesday during a visit to Tashkent, quoted by Anadolu.

It comes after a top-level Turkish delegation led by foreign ministry undersecretary Umit Yalcin went to Baghdad on Monday.

Late Tuesday, the Turkish foreign ministry reissued its travel guidance from December 2015 to its citizens, warning against travelling to Iraq because of the security risk.

The advice applied to all provinces except Dohuk, Arbil and Sulaymaniyah, all of which are in the northern region of Iraqi Kurdistan.

Those currently in the country were strongly advised to withdraw from areas including Baghdad and Basra, referring to the latest developments in Mosul.

The ministry urged its citizens in a statement on its website to be vigilant, avoid crowded places and limit the time of travel in 15 provinces including Kirkuk, Anbar and Najaf.